TSTP Solution File: KRS256+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS256+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:45:20 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS256+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 10:33:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(status_type, type, (
% 0.19/0.48 status: ( $i * $i * $i ) > $o)).
% 0.19/0.48 tff(thm_type, type, (
% 0.19/0.48 thm: $i)).
% 0.19/0.48 tff(tptp_fun_C_33_type, type, (
% 0.19/0.48 tptp_fun_C_33: $i)).
% 0.19/0.48 tff(esa_type, type, (
% 0.19/0.48 esa: $i)).
% 0.19/0.48 tff(model_type, type, (
% 0.19/0.48 model: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_I2_1_type, type, (
% 0.19/0.48 tptp_fun_I2_1: $i > $i)).
% 0.19/0.48 tff(tptp_fun_I1_0_type, type, (
% 0.19/0.48 tptp_fun_I1_0: $i > $i)).
% 0.19/0.48 tff(tptp_fun_I1_35_type, type, (
% 0.19/0.48 tptp_fun_I1_35: $i)).
% 0.19/0.48 tff(tptp_fun_I2_36_type, type, (
% 0.19/0.48 tptp_fun_I2_36: $i)).
% 0.19/0.48 tff(tptp_fun_Ax_34_type, type, (
% 0.19/0.48 tptp_fun_Ax_34: $i)).
% 0.19/0.48 tff(mighta_type, type, (
% 0.19/0.48 mighta: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_C_18_type, type, (
% 0.19/0.48 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_Ax_19_type, type, (
% 0.19/0.48 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_I1_3_type, type, (
% 0.19/0.48 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.19/0.48 tff(1,assumption,(![I2: $i] : (~model(I2, C!33))), introduced(assumption)).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (((model(I1!35, Ax!34) & model(I1!35, C!33)) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))) <=> (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C)))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 (model(I1!35, C!33)),
% 0.19/0.48 inference(and_elim,[status(thm)],[6])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 ((~![I2: $i] : (~model(I2, C!33))) | (~model(I1!35, C!33))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[8, 7, 1])).
% 0.19/0.48 tff(10,plain,(~![I2: $i] : (~model(I2, C!33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(11,assumption,(![I1: $i] : (~model(I1, C!33))), introduced(assumption)).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 ((~![I1: $i] : (~model(I1, C!33))) | (~model(I1!35, C!33))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[12, 7, 11])).
% 0.19/0.48 tff(14,plain,(~![I1: $i] : (~model(I1, C!33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 ((~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))) | ![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 ((~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))) | ![I2: $i] : (~model(I2, C!33))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33))))) | (![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 ((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (^[Ax: $i, C: $i] : refl((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (^[Ax: $i, C: $i] : rewrite((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) <=> ((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))), rewrite(((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))) <=> ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))), rewrite((((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (^[Ax: $i, C: $i] : rewrite(((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(30,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','esa')).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.49 tff(32,plain,(
% 0.19/0.49 ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[31])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa))) | (~((~status(C!33, C!33, esa)) | (~((~(model(tptp_fun_I2_1(C!33), C!33) | ![I1: $i] : (~model(I1, C!33)))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, C!33))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (~((~((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa))) | (~((~status(C!33, C!33, esa)) | (~((~(model(tptp_fun_I2_1(C!33), C!33) | ![I1: $i] : (~model(I1, C!33)))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, C!33)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (((~((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa))) | (~((~status(C!33, C!33, esa)) | (~((~(model(tptp_fun_I2_1(C!33), C!33) | ![I1: $i] : (~model(I1, C!33)))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, C!33))))))))) | ((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 ((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 ((~((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa))) | (~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 ((~((~(model(tptp_fun_I1_0(C!33), C!33) | model(tptp_fun_I2_1(C!33), C!33))) | (~(![I1: $i] : (~model(I1, C!33)) | ![I2: $i] : (~model(I2, C!33)))))) | status(C!33, C!33, esa)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (status(C!33, C!33, esa)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[41, 19])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(53,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mighta')).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.49 tff(55,plain,(
% 0.19/0.49 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[54])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 ((~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))) <=> (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 (((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))) | (mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 (mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 ((~mighta(esa, thm)) <=> (~mighta(esa, thm))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(69,axiom,(~mighta(esa, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_esa_thm')).
% 0.19/0.49 tff(70,plain,
% 0.19/0.49 (~mighta(esa, thm)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 ((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 ((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | ((~status(C!33, C!33, esa)) | (~status(C!33, C!33, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | (~status(C!33, C!33, esa)) | (~status(C!33, C!33, thm)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | ((~status(C!33, C!33, esa)) | (~status(C!33, C!33, thm)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | (~status(C!33, C!33, esa)) | (~status(C!33, C!33, thm))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.49 tff(77,plain,
% 0.19/0.49 (~status(C!33, C!33, thm)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[76, 73, 42])).
% 0.19/0.49 tff(78,plain,
% 0.19/0.49 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.49 tff(80,plain,
% 0.19/0.49 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.49 tff(90,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','thm')).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.50 tff(93,plain,(
% 0.19/0.50 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[92])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[95, 79])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!33, C!33, thm)) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!33, C!33, thm))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 ((~(~status(C!33, C!33, thm))) <=> status(C!33, C!33, thm)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 (((~status(C!33, C!33, thm)) | $false) <=> (~status(C!33, C!33, thm))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 ((~$true) <=> $false),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 (((~status(C!33, C!33, thm)) | $true) <=> $true),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 (![I1: $i] : $true <=> $true),
% 0.19/0.50 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (![I1: $i] : $true <=> $true),
% 0.19/0.50 inference(transitivity,[status(thm)],[103, 102])).
% 0.19/0.50 tff(105,plain,
% 0.19/0.50 (^[I1: $i] : rewrite(((~model(I1, C!33)) | model(I1, C!33)) <=> $true)),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(106,plain,
% 0.19/0.50 (![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)) <=> ![I1: $i] : $true),
% 0.19/0.50 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.50 tff(107,plain,
% 0.19/0.50 (![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)) <=> $true),
% 0.19/0.50 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 (((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))) <=> ((~status(C!33, C!33, thm)) | $true)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 (((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))) <=> $true),
% 0.19/0.50 inference(transitivity,[status(thm)],[108, 101])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 ((~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)))) <=> (~$true)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 ((~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)))) <=> $false),
% 0.19/0.50 inference(transitivity,[status(thm)],[110, 100])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 ((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) <=> (~status(C!33, C!33, thm))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))))) <=> ((~status(C!33, C!33, thm)) | $false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[112, 111])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 (((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))))) <=> (~status(C!33, C!33, thm))),
% 0.19/0.50 inference(transitivity,[status(thm)],[113, 99])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 ((~((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)))))) <=> (~(~status(C!33, C!33, thm)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 ((~((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33)))))) <=> status(C!33, C!33, thm)),
% 0.19/0.50 inference(transitivity,[status(thm)],[115, 98])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!33, C!33, thm))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!33, C!33, thm))),
% 0.19/0.50 inference(transitivity,[status(thm)],[117, 97])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!33, C!33), C!33)) | model(tptp_fun_I1_3(C!33, C!33), C!33))) | status(C!33, C!33, thm))) | (~((~status(C!33, C!33, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, C!33))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(C!33, C!33, thm)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[120, 96, 77])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------